Question

If a rectangular field of an area $100$ square units is divided into two parts of area $36$ square units and $64$ square units along the length such that the length of the original field and both the newly created fields are coprime to each other, then the sum of the length of original field and both the newly created fields is

Answer 1

$100=2^2\times 5^2$
$64=2^6$
$36=2^2\times 3^2$
Since, the common factor among all is $2^2$
So, the breadth is $2^2=4$ and the lengths are
$100=4\times 25$
$64=4\times 16$
$36=4\times 9$
So, sum is $25+16+9=50$ units